1. A Zero-Order Picture of the Jahn-Teller Coupled Region of the Infrared Spectrum of CH3O and CD3O
Britta A. Johnson and Edwin L. Sibert III
University of Wisconsin—Madison
International Symposium on Molecular Spectroscopy
Urbana-Champaign
Thursday, June 23, 2016

2. Methoxy Radical Methoxy has a doubly degenerate ground state (X2E)
Therefore, moderate JT coupling with respect to three vibrational e modes
Also experiences small spin-orbit coupling
C3v Cs

3. Create Hamiltonian/Potential Fit
Developed fitted quartic potential force field (based upon scans taken using CCSD(T)/cc-pVTZ)
Generated Hamiltonian which includes
Jahn-Teller coupling
Fermi coupling
Anharmonicity
Barckholtz, T. A.; Miller, T. A. Int. Rev. Phys. Chem. 1998, 17,

4. CH3O Spectra: Comparison to Experiment
Lee Y.-F.; Chou W.-T.; Johnson, B. A.; Tabor, D. P.; Sibert, E. L.; Lee Y.-P J. Mol. Spectrosc. 2015, 310,

5. Eighteenth Excited State
Decomposition of eighteenth excited state into normal mode basis.

6. Normal Modes:
Modes 2, 3, 5, and 6 are important for this region of the spectrum.
Mode
Symmetry
Wavenumber (cm-1)
Description 1 a1
CH stretch 2
Umbrella 3
CO stretch 4 e 5
HCH bend 6
CHO rock
Modes 5 and 6 are the strongest Jahn-Teller coupled modes.

7. Full Correlation Diagram

8. Partitioned Hamiltonian

9. Partitioned Hamiltonian

10. Partitioned Hamiltonian

11. Partitioned Hamiltonian

12. Partitioned Hamiltonian
Everything else is included here:
Higher order JT terms
Fermi coupling
Etc.

13. Partitioned Hamiltonian

14. Partitioned Hamiltonian

15. Construct the Zero-Order Hamiltonian, H0
Two degenerate electronic surfaces: treat as diabats.
As first approximation, place 9 harmonic normal modes on each diabat with Morse oscillator to model CH stretches
Q6x

16. The Zero-Order Hamiltonian, H0
Two degenerate electronic surfaces: treat as diabats.

17. Zero-Order Hamiltonian, H0
Two degenerate electronic surfaces: treat as diabats.
This form is extended to the other 6 modes in the system.
No coupling between electronic surfaces

18. Eighteenth Excited State (2009 cm-1)B C D E F G
Overlap diagrams are used to measure quality of representation
Decomposition of eigenstate into the zero-order basis
The I2 is the “percentage” of the eigenstate that is made up of that zero-order state

19. Eighteenth Excited State (2009 cm-1)B C D E F G
Inverse Participation Number:
Roughly the number of zero-order states need to represent the eigenstate

20. Eigthteenth Excited State (2009 cm-1)B C D E F G

21. Linear JT Coupling in Mode 6
The potential (only with respect to mode 6):
Now have off-diagonal coupling between the two electronic states.
Diagonalizable (diabatic to adiabatic transformation)

22. Shape of Potentials Q5/Q6 representation Q6x/Q6y representation
Upper Adiabat Lower Adiabat
Upper Adiabat Lower Adiabat Q6
Q6y Q5 Q5
Q6x
Q6x
Each coordinates ranges 0 to 3
Each coordinates ranges -3 to 3

23. Eigthteenth Excited State (2009 cm-1)B C D E F G

24. Zero-Order Hamiltonian: H1JT6

25. Zero-Order Hamiltonian: H1JT6

26. Linear and Quadratic Coupling in Mode 6
Upper Adiabat Lower Adiabat
Q6x/Q6y representation

27. Zero-Order Hamiltonian: H1JT6
Have three options:
1. Include linear and quadratic coupling in mode 6

28. Eigthteenth Excited State (2009 cm-1)K L

29. Zero-Order Hamiltonian: H1JT6
Have three options:
1. Include linear and quadratic coupling in mode 6
2. Include linear coupling in mode 5 and mode 6

30. Zero-Order Hamiltonian-Linear JT in Mode 5 and 6
For a single mode
This has logical extension to include a second linear Jahn-Teller coupled mode (mode 5)
Diagonalize

31. Zero-Order Hamiltonian-Linear JT in Mode 5 and 6
For a single mode
This has logical extension to include a second linear Jahn-Teller coupled mode (mode 5)
Diagonalize

32. Eigthteenth Excited State (2009 cm-1)J

33. Zero-Order Hamiltonian: H1JT6
Have three options:
1. Include linear and quadratic coupling in mode 6
2. Include linear coupling in mode 5 and mode 6
3. Include linear and quadratic JT in mode 5 and 6

34. Zero-Order Hamiltonian: HJT

35. Participation Numbers for CH3O
l = 1
l = 0

36. CD3O: Can we use the same method?
Lee Y.-F.; Chou W.-T.; Johnson, B. A.; Tabor, D. P.; Sibert, E. L.; Lee Y.-P J. Mol. Spectrosc. 2015, 310,

37. CD3O: Can we use the same method?
Here we have a new type of Jahn-Teller coupling which we have separated.

38. CD3O: Can we use the same method?

39. CD3O: Can we use the same method?B

40. Conclusions:
We developed a potential force field that reproduces the experimental spectra for CH3O and CD3O
We partitioned the correlation diagram to study the effects different coupling elements have on eigenstates.
By creating a series of zero-order Hamiltonians, we are able to visualize the decomposition of eignestates into the zero-order states.

41. Acknowledgements Sibert Group Y.P. Lee’s Group NSF Ned Sibert
Danny Tabor
Dr. Jayashree Nagesh
Y.P. Lee’s Group
NSF